Modeling without using phase-information and robust stability

Abstract

Discusses modeling for robust control. To keep the input-output property, we need the error small to make the sensitivity function small in a specified frequency range with robust stability. We considered the condition to make the sensitivity function small in a specified function range with robust stability. It is shown that the numbers of unstable poles, zeros and relative degree are required. We call the number of relative degrees and unstable zeros the phase-information because this relates the phase of the plant. We may not measure the phase-information of real plants. We propose a procedure to select the nominal model to make the sensitivity function small in a specified frequency range with robust stability without using phase-information. First the sensitivity function with desirable property is selected. The conditions of the nominal plant to satisfy the robust stability condition with preassigned sensitivity property is considered. Next how to select the nominal plant is invented. A design method of control systems with robust stability and preassigned sensitivity property is presented.